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Theorem syl9 70
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Hypotheses
Ref Expression
syl9.1 (𝜑 → (𝜓𝜒))
syl9.2 (𝜃 → (𝜒𝜏))
Assertion
Ref Expression
syl9 (𝜑 → (𝜃 → (𝜓𝜏)))

Proof of Theorem syl9
StepHypRef Expression
1 syl9.1 . 2 (𝜑 → (𝜓𝜒))
2 syl9.2 . . 3 (𝜃 → (𝜒𝜏))
32a1i 9 . 2 (𝜑 → (𝜃 → (𝜒𝜏)))
41, 3syl5d 66 1 (𝜑 → (𝜃 → (𝜓𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  syl9r  71  com23  76  sylan9  395  pm4.79dc  820  pclem6  1281  bilukdc  1303  sbequi  1736  reuss2  3245  reupick  3249  elres  4674  funimass4  5252  fliftfun  5464  elabgf2  10306  bj-rspgt  10312
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